The gains were led by banking, realty, consumer durable and PSU stocks, while information technology stocks declined.
The rupee also gained on the back of Rajan's announcements and went up to 65.5 against the dollar in intra-day trade from yesterday's close of 67.07.
The index opened 290 points higher than yesterday's close and gained as much as 550 points to the day's high of 19,117.52 before settling at 18,979.76, a rise of 412.21 points or 2.22 per cent.
Soon after taking over as the 23rd Governor of the Reserve Bank of India, Rajan announced plans to revise and strengthen the monetary policy framework and liberalise the markets as well as curbs on investment and position-taking.
He said steps would be taken to strengthen financial infrastructure and attract capital inflows and stressed the need for faster, broad based, inclusive growth.
"The RBI governor's enthusiastic words seemed to calm the markets," said Raghu Kumar, co-founder of RKSV Securities. "Mr Rajan emphasised that the RBI's primary role is to keep inflation levels at bay and to keep stability in the markets."
The National Stock Exchange index Nifty shot up 144.85 points, or 2.66 per cent to 5,592.95. The MCX-SX's SX-40 ended at 11,208.21, up 241.39 points.
The passage of the Pension Bill in the Lok Sabha yesterday raised hopes of more reforms, experts said.
